18,389 research outputs found
Simultaneous Reduced Basis Approximation of Parameterized Elliptic Eigenvalue Problems
The focus is on a model reduction framework for parameterized elliptic
eigenvalue problems by a reduced basis method. In contrast to the standard
single output case, one is interested in approximating several outputs
simultaneously, namely a certain number of the smallest eigenvalues. For a fast
and reliable evaluation of these input-output relations, we analyze a
posteriori error estimators for eigenvalues. Moreover, we present different
greedy strategies and study systematically their performance. Special attention
needs to be paid to multiple eigenvalues whose appearance is
parameter-dependent. Our methods are of particular interest for applications in
vibro-acoustics
Black String Entropy and Fourier-Mukai Transform
We propose a microscopic description of black strings in F-theory based on
string duality and Fourier-Mukai transform. These strings admit several
different microscopic descriptions involving D-brane as well as M2 or M5-brane
configurations on elliptically fibered Calabi-Yau threefolds. In particular our
results can also be interpreted as an asymptotic microstate count for D6-D2-D0
configurations in the limit of large D2-charge on the elliptic fiber. The
leading behavior of the microstate degeneracy in this limit is shown to agree
with the macroscopic entropy formula derived from the black string supergravity
solution.Comment: 22 pages, latex; v2: substantial revision of the macroscopic
description of the system; results essentially unchange
Equivalence of several descriptions for 6d SCFT
We show that the three different looking BPS partition functions, namely the
elliptic genus of the 6d gauge theory with
flavors and a tensor multiplet, the Nekrasov partition function of the 5d
gauge theory with flavors, and the Nekrasov
partition function of the 5d gauge theory with
flavors, are all equal to each other under specific maps among gauge theory
parameters. This result strongly suggests that the three gauge theories have an
identical UV fixed point. Type IIB 5-brane web diagrams play an essential role
to compute the Nekrasov partition function as well as establishing the
maps.Comment: v1: 40 pages, 13 figures, v2: published versio
Multiscale Partition of Unity
We introduce a new Partition of Unity Method for the numerical homogenization
of elliptic partial differential equations with arbitrarily rough coefficients.
We do not restrict to a particular ansatz space or the existence of a finite
element mesh. The method modifies a given partition of unity such that optimal
convergence is achieved independent of oscillation or discontinuities of the
diffusion coefficient. The modification is based on an orthogonal decomposition
of the solution space while preserving the partition of unity property. This
precomputation involves the solution of independent problems on local
subdomains of selectable size. We deduce quantitative error estimates for the
method that account for the chosen amount of localization. Numerical
experiments illustrate the high approximation properties even for 'cheap'
parameter choices.Comment: Proceedings for Seventh International Workshop on Meshfree Methods
for Partial Differential Equations, 18 pages, 3 figure
A reduced basis localized orthogonal decomposition
In this work we combine the framework of the Reduced Basis method (RB) with
the framework of the Localized Orthogonal Decomposition (LOD) in order to solve
parametrized elliptic multiscale problems. The idea of the LOD is to split a
high dimensional Finite Element space into a low dimensional space with
comparably good approximation properties and a remainder space with negligible
information. The low dimensional space is spanned by locally supported basis
functions associated with the node of a coarse mesh obtained by solving
decoupled local problems. However, for parameter dependent multiscale problems,
the local basis has to be computed repeatedly for each choice of the parameter.
To overcome this issue, we propose an RB approach to compute in an "offline"
stage LOD for suitable representative parameters. The online solution of the
multiscale problems can then be obtained in a coarse space (thanks to the LOD
decomposition) and for an arbitrary value of the parameters (thanks to a
suitable "interpolation" of the selected RB). The online RB-LOD has a basis
with local support and leads to sparse systems. Applications of the strategy to
both linear and nonlinear problems are given
Algorithms and data structures for adaptive multigrid elliptic solvers
Adaptive refinement and the complicated data structures required to support it are discussed. These data structures must be carefully tuned, especially in three dimensions where the time and storage requirements of algorithms are crucial. Another major issue is grid generation. The options available seem to be curvilinear fitted grids, constructed on iterative graphics systems, and unfitted Cartesian grids, which can be constructed automatically. On several grounds, including storage requirements, the second option seems preferrable for the well behaved scalar elliptic problems considered here. A variety of techniques for treatment of boundary conditions on such grids are reviewed. A new approach, which may overcome some of the difficulties encountered with previous approaches, is also presented
Modelling and simulation of a biometric identity-based cryptography
Government information is a vital asset that must be kept in a trusted environment and efficiently managed by authorised parties. Even though e-Government provides a number of advantages, it also introduces a range of new security risks. Sharing confidential and top-secret information in a secure manner among government sectors tend to be the main element that government agencies look for. Thus, developing an effective methodology is essential and it is a key factor for e-Government success. The proposed e-Government scheme in this paper is a combination of identity-based encryption and biometric technology. This new scheme can effectively improve the security in authentication systems, which provides a reliable identity with a high degree of assurance. In addition, this paper demonstrates the feasibility of using Finite-state machines as a formal method to analyse the proposed protocols
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